Well, I'm afraid I can tell you that Willie wasn't a son of John Marshall Rigsby. John M was born in 1839 and had children beginning in 1859. I knew his wife was Mary Elizabeth, but hadn't yet found her maiden name. Thanks for the help.
The only Rigsbys in AL in 1820 were Enoch and Thomas, who were listed in Dallas Co on the 1820 state census. There was also a Francis who married Elizabeth Roper in Mobile Co in 1818, but I've never seen anything more about him. In 1830 there aren't any Rigsbys in AL, but there is an E Rigby in Dallas Co AL and an Enoch Rigby in Houston Co GA. In 1840 Enoch Rigsby is in Randolph Co GA. I haven't found him in 1850, but in 1860 and 1870 he is in Butler Co AL. Thomas doesn't appear after the 1820 census, that I can find.
Enoch had two sons born before 1830 whom I haven't been able to identify. Willie may have been one of them. The times and locations approximately fit.
I'll let you know if I find anything more about him. Do you know if Martha had any siblings? Many of the Rigsby families had names that were frequently used. That might be another clue.